Simple Explanation of Zipf's Mystery via New Rank-Share Distribution, Derived from Combinatorics of the Ranking Process

32 Pages Posted: 21 Feb 2017

Date Written: February 15, 2017

Abstract

This work provides a surprisingly simple explanation of Zipf’s law and derives an exact formula for Zipf’s distribution. It also presents a new rank-share distribution and illustrates that peculiar dependency between a share and 1/rank, observed in many publications, is descended from expected values of various ranks in the new distribution. All conclusions, formulas and charts presented here were tested against publicly available statistical data in different areas. The correlation between predicted and observed dependences are really impressive. For large datasets (> million records), the average correlation coefficients were (R=0.999, R2 = 0.997, Theil's U2 = 0.0135). Monte-Carlo simulations were performed as the additional evidence.

Keywords: Zipf, Explanation, Formula, Rank, Share, Distribution

JEL Classification: C40, C60, D30, D40, R11, R12, R15

Suggested Citation

Shyklo, Alexandra, Simple Explanation of Zipf's Mystery via New Rank-Share Distribution, Derived from Combinatorics of the Ranking Process (February 15, 2017). Available at SSRN: https://ssrn.com/abstract=2918642 or http://dx.doi.org/10.2139/ssrn.2918642

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